We develop a relativistic framework to investigate the evolution of cosmological structures from the initial density perturbations to the highly nonlinear regime. Our approach involves proposing a procedure to match “best-fit,” exact Bianchi IX (BIX) spacetimes to finite regions within the perturbed Friedmann-Lemaître-Robertson-Walker universe, characterized by a positive averaged spatial curvature. This method enables us to approximately track the nonlinear evolution of the initial perturbation using an exact solution. Unlike standard perturbation theory and exact solutions with a high degree of symmetry (such as spherical symmetry), our approach is applicable to generic initial data, with the only requirement being positive spatial curvature. By employing the BIX symmetries, we can systematically incorporate the approximate effects of shear and curvature into the process of collapse. Our approach addresses the limitations of both standard perturbation theory and highly symmetric exact solutions, providing valuable insights into the nonlinear evolution of cosmological structures.

Detecting stochastic gravitational wave backgrounds (SGWBs) with the Laser Interferometer Space Antenna (LISA) is one of the mission’s scientific objectives. Disentangling SGWBs of astrophysical and cosmological origin is a challenging task, further complicated by the noise level uncertainties. In this study, we present a Bayesian methodology for inferring SGWBs, drawing inspiration from Gaussian stochastic processes. We assess the effectiveness of this approach for signals with unknown spectral shapes by systematically exploring the model hyperparameters—a preliminary step toward a more efficient transdimensional exploration. To validate our method, we apply it to a representative astrophysical scenario: the inference of the astrophysical background of extreme mass ratio inspirals, as recently estimated [F. Pozzoli et al., Phys. Rev. D 108, 103039 (2023)]. Our findings indicate that the algorithm is capable of recovering the injected signal even with uninformative priors, simultaneously providing an estimate of the noise level.

The LHAASO Collaboration has recently reported a measurement of the diffuse gamma-ray emission from the Galactic Plane at energies between 10 TeV and 1 PeV. While this emission is brighter than that expected from cosmic-ray interactions in the interstellar medium alone, we show that the intensity, spectrum, and morphology of this excess are in good agreement with that predicted from the “TeV halos” which surround the Milky Way’s pulsar population. These results support the conclusion that TeV halos dominate the ultrahigh-energy sky, and that these objects convert $\sim 5\%$ of their total spindown power into very high and ultrahigh-energy photons.

In this paper we study the universal properties of the baryon chemical potential Fourier coefficients in quantum chromodynamics. We show that by following a well-defined strategy, the Fourier coefficients can be used to locate Yang-Lee edge singularities associated with chiral phase transition (and by extension with the Roberge-Weiss) in the complex chemical potential plane. We comment on the viability of performing this analysis using lattice QCD data.

Following our previous study of the recursive structure of Baikov representations, we discuss its application in the integration-by-parts reduction of Feynman integrals. We combine the top-down reduction approach with the recursive structure, which can greatly simplify the calculation for each sector in many cases. We introduce a new concept called the top-sector irreducible scalar product reduction, which generalizes the maximal-cut reduction by retaining the subsector information. After subtracting the top-sector components, we provide a general method to transform the remaining integrand explicitly to subsectors, such that the reduction procedure can be carried out recursively. In this work, we use the intersection theory to demonstrate our method, although it can be applied to any implementation of the integration-by-parts reduction.

The precision with which hadronic vacuum polarization (HVP) is obtained determines how accurately important observables, such as the muon anomalous magnetic moment $a_{\mu }$ or the low-energy running of the electromagnetic coupling $\alpha$, are predicted. The two most precise approaches for determining HVP are dispersive relations combined with $e^{+}{e}^{-}\to \text{hadrons}$ cross section data and lattice QCD. However, the results obtained in these two approaches display significant tensions, whose origins are not understood. Here we present a framework that sheds light on this issue and—if the two approaches can be reconciled—allows them to be combined. Via this framework, we test the hypothesis that the tensions can be explained by modifying the R-ratio in different intervals of center-of-mass energy $\sqrt{s}$. As ingredients, we consider observables that have been precisely determined in both approaches. These are the leading hadronic contributions to $a_{\mu }$, to the so-called intermediate window observable, and to the running of $\alpha$ between spacelike virtualities 1 and $10{\mathrm{GeV}}^2$ (for which only a preliminary lattice result exists). Our tests take into account all uncertainties and correlations, as well as uncertainties on uncertainties in the lattice results. For instance, using this framework we show that results obtained in the two approaches can be made to agree, for all three observables, by modifying the $\rho$ peak in the experimental spectrum. More specifically, we show that this requires a common $\sim 5\%$ increase in the contributions of the peak to each of the three observables. This result is robust against the presence or absence of the running of $\alpha$ in the comparison. However, such an increase is much larger than the uncertainties on the measured R-ratio. We also discuss a variety of generalizations of the methods used here, as well as the limits in the information that can be extracted from the R-ratio via a finite set of observables.

One of the most well-founded candidates for dark matter remains a split-supersymmetry (SUSY) model with a Higgsino- or winolike lightest superpartner and the grander SUSY model providing answers for the hierarchy problem and grand unified theory scale unification. The relatively heavy scalar superpartners imply such models would not yet be seen at collider experiments, and mixing-suppressed couplings place such models outside the reach of current direct detection experiments. As such particles annihilate fairly readily to electroweak bosons, a significant neutrino signal can arise near the Galactic Center that may be visible to dedicated searches at current and future neutrino telescopes.

The addition of a Higgs quadruplet to the standard model (SM) of quarks and leptons would shift the $W$-boson mass upward. It could also facilitate the production of dark matter through the conventional thermal freeze-out scenario via Yukawa interaction with the Higgs quadruplet or freeze-in production from the decay of SM Higgs. We investigate the same-sign lepton smoking gun signature of the double-charged scalar component of the quadruplet Higgs at the LHC.

The predictivity of many nonthermal dark matter (DM) models is marred by the gravitational production background. Nevertheless, if the reheating temperature $T_R$ is low, the gravitationally produced relics can be diluted. We study the freeze-in dark matter production mechanism at temperatures below the dark matter mass. In this case, the coupling to the thermal bath has to be significant to account for the observed dark matter relic density. As a result, the direct DM detection experiments already probe such freeze-in models, excluding significant parts of parameter space.

A future $e^{+}{e}^{-}$ circular collider (FCC-ee) may provide a unique probe of the electron Yukawa coupling through Higgs boson production on resonance. Motivated by this exciting possibility, we examine a simple model which can result in $\mathcal{O}(10)$ modifications of the Higgs coupling to electrons. The model can also lead to deviations in the electron anomalous magnetic moment, $g_e-2$, which at present shows a $+2.2\sigma$ or $-3.7\sigma$ deviation, implied by differing precision determinations of the electromagnetic fine structure constant. The electron $g_e-2$ can be a forerunner for FCC-ee discoveries which, as we elucidate, may not be accessible to the high-luminosity LHC measurements. A simple extension of our model can also account for the current deviation in the muon $g_{\mu }-2$.

Nuclear recoil from scattering with weakly interacting massive particles (WIMPs) is a signature searched for in direct detection of dark matter. The underlying WIMP-nucleon interactions could be spin and/or orbital angular momentum (in)dependent. Evaluation of nuclear recoil rates through these interactions requires accounting for nuclear structure, e.g., through shell model calculations. We evaluate nuclear response functions induced by these interactions for ${}^{19}\mathrm{F}$, ${}^{23}\mathrm{Na}$, ${}^{28,29,30}\mathrm{Si}$, ${}^{40}\mathrm{Ar}$, ${}^{70,72,73,74,76}\mathrm{Ge}$, ${}^{127}\mathrm{I}$, and ${}^{128,129,130,131,132,134,136}\mathrm{Xe}$ nuclei that are relevant to current direct detection experiments, and estimate their sensitivity to shell model interactions. Shell model calculations are performed with the NuShellX solver. Nuclear response functions from nonrelativistic effective field theory are evaluated and integrated over transferred momentum for quantitative comparisons. We show that although the standard spin-independent response is barely sensitive to the structure of the nuclei, large variations with the shell model interaction are often observed for the other channels. Significant uncertainties may arise from the nuclear components of WIMP-nucleus scattering amplitudes due to nuclear structure theory and modeling. These uncertainties should be accounted for in analyses of direct detection experiments.

We propose a modified Wasserstein generative adversarial network (M-WGAN) to study the distribution of the topological charge in lattice QCD based on Monte Carlo simulations. We construct new generator and discriminator in M-WGAN to support the generation of high-quality distribution. Our results show that the M-WGAN scheme of machine learning should be helpful for us to calculate efficiently the 1D distribution of topological charge compared with the method by the Monte Carlo simulation alone.

Inspired by the resonance $T_{cc}^{+}(3875)$ recently observed by the LHCb Collaboration, we systematically explore the $S$- and $P$-wave $cc\overline{q}{\overline{q}}^{\prime }$ $(\overline{q},{\overline{q}}^{\prime }=\overline{u},\overline{d},\overline{s})$ systems in a chiral SU(3) quark model. The Hamiltonian contains the kinetic energy, the one-gluon-exchange (OGE) potential, the confinement potential, and the one-boson-exchange (OBE) potential stemming from the coupling of quark and chiral fields. The Schrödinger equation is solved by use of the variational method with the spacial trial wave functions chosen as Gaussian functions. It is found that the lowest state has a mass 3879 MeV, isospin and spin-parity $I{J}^P=01^{+}$, and quark constituent $cc\overline{u}\overline{d}$, in agreement with the experimentally observed $T_{cc}^{+}(3875)$. This state is approximately at the calculated $D{D}^{*}$ threshold and has a root-mean-square radius of about 0.48 fm. These demonstrate that the $T_{cc}^{+}(3875)$ can be accommodated as a stable and compact tetraquark sate in the chiral SU(3) quark model. All the other $S$- and $P$-wave $cc\overline{q}{\overline{q}}^{\prime }$ $(\overline{q},{\overline{q}}^{\prime }=\overline{u},\overline{d},\overline{s})$ states lie about 100 to a few hundreds MeV higher than the corresponding meson-meson thresholds and thus are not suggested to be candidates of stable and compact tetraquark states due to their fall-apart decays to two mesons.

We discuss the spectrum and the internal composition of ground and excited four-quark states in the charm and bottom energy region. To this end we extend previous calculations within the framework of the relativistic four-body Faddeev-Yakubovsky equation to include quantum numbers with $J^{PC}=0^{++},0^{-+},1^{--},1^{+-}$ and $1^{++}$ and study their internal composition in terms of heavy-light meson pairs, hadroquarkonia and diquark-antidiquark clusters. We observe similar patterns in the charm and bottom energy region with different compositions of the four-quark states depending on $J^{PC}$ quantum numbers. Most notably, we find that all states with $C·P=+1$ are dominated by heavy-light meson contributions, whereas for axial-vector states with $J^{PC}=1^{+-}$ including the $Z_c(3900)$ we find a much more complicated picture depending on the flavor content. We systematically compare our results for the spectrum with existing experimental results and provide predictions for future analyses.

We study the extraction of transition generalized parton distributions (GPDs) from production of two back-to-back high transverse momentum photons ($\gamma \gamma$) and a massive pair of leptons (${\ell }^{+}{\ell }^{-}$) in hard exclusive pion-nucleon scattering. We argue that the exclusive scattering amplitude of both processes could be factorized into nonperturbative pion distribution amplitude and nucleon transition GPDs that are convoluted with perturbatively calculable short-distance matching coefficients. We demonstrate that the exclusive diphoton production not only is complementary to the Drell-Yan-type dilepton production for extracting the GPDs but also provides enhanced sensitivities for extracting the parton momentum fraction $x$ dependence of the GPDs. We show that both exclusive observables are physically measurable at the J-PARC and AMBER experiment energies. If the target nucleon can be polarized, corresponding spin asymmetries can offer additional sensitivities for extracting transition GPDs.

We study the phase structure of five-dimensional Yang-Mills theories coupled to Dirac fermions. In order to tackle their nonperturbative character, we derive the flow equations for the gauge coupling and the effective potential for the Aharonov-Bohm phases employing the functional renormalization group. We analyze the infrared and ultraviolet fixed-point solutions in the flow of the gauge coupling as a function of the compactification radius of the fifth dimension. We discuss various types of trajectories which smoothly connect both dimensional limits. Last, we investigate the phase diagram and vacuum structure of the gauge potential for different fermion content.

We consider the interplay of the muon $g-2$ anomaly and the proton decay in the supersymmetry (SUSY) SU(5) grand unified theories (GUTs) with generation-independent scalar soft masses. In these scenarios, we introduce a number of $\mathbf{5}+\overline{\mathbf{5}}$ messenger fields with doublet-triplet splitting in general gauge mediation to transmit SUSY breaking to the visible sector by gauge loops. As a result, squarks and sleptons receive generation-independent soft SUSY breaking masses, which are split already at the messenger scale. Taking into account the perturbative unification of gauge couplings as well as the bounds from electroweak precision and vacuum stability bounds, we showed the parameter space in general gauge mediation to explain the muon $g-2$ anomaly with smuon and sneutrino loops while evading the strong bounds on squarks and gluinos from the Large Hadron Collider. We also obtained the dominant Higgsino contributions to the proton decay mode, $p\to K^{+}\overline{\nu }$, with general generation-independent sparticle masses for squarks and sleptons. Even for split scalar soft masses in our model, however, we found that the bounds from the proton decay are satisfied only if the effective Yukawa couplings of the colored Higgsinos are suppressed further by a factor of order ${10}^{-4}–{10}^{-3}$. We illustrated how such a suppression factor is realized in orbifold GUTs in the extra dimension where the colored Higgsinos in the bulk are not coupled to the matter fields localized at the orbifold fixed points at the leading order.

The gauge-boson, ghost and fermion propagators as well as the gauge-boson-ghost vertex function are studied for $\mathrm{SU}(N)$, $\mathrm{Sp}(2N)$, and $\mathrm{SO}(N)$ gauge groups. We solve a set of coupled Dyson-Schwinger equations in Landau gauge for a variable, fractional number $N_f$ of massless fermions in the fundamental representation. For large $N_f$ we find a phase transition from a chirally broken into a chirally symmetric phase that is consistent with the behavior expected inside the conformal window. Even in the presence of fermions the gauge-boson-ghost-vertex dressing remains small. In the conformal window this vertex shows the expected power law behavior. It does not assume its tree-level value in the far infrared, but the respective dressing function is a constant greater than 1.

Canonical quantization of the photon—a free massless vector field—is considered in cosmological spacetimes in a two-parameter family of linear gauges that treat all the vector potential components on equal footing. The goal is setting up a framework for computing photon two-point functions appropriate for loop computations in realistic inflationary spacetimes. The quantization is implemented without relying on spacetime symmetries, but rather it is based on the classical canonical structure. Special attention is paid to the quantization of the canonical first-class constraint structure that is implemented as the condition on the physical states. This condition gives rise to subsidiary conditions that the photon two-point functions must satisfy. Some of the de Sitter space photon propagators from the literature are found not to satisfy these subsidiary conditions, bringing into question their consistency.